Originally posted by jawats in some ways, it comes down to adjusting expectations for a 280mm (200mm with 1.4x TC) lens at some distance from the bird.
Definitely. And with a FF sensor, with lower pixel density than a KP or K-3iii. Even on an APS-C camera, 300mm is generally just the starting point for photographing birds in the wild, unless you can get unusually close. But that's just part of the trade-off. Carrying around a 2kg lens can detract from the experience too. So it's worth exploring how to get better results with what you have.
I agree with what others have said about the overexposure. For birding I usually use centre-weighted or spot metering, but in this situation it would only have exacerbated the over-exposure, because it would have weighted the exposure for the bird rather than the sky. Probably better to use matrix metering and bring up the exposure of the bird in post. Or (although it sound counter-intuitive) use fill flash. If you weren't too far away, and you had a reasonably powerful flash with HSS, it would add a bit of light to the bird and give more colour and detail. This would help with contrast, which is lacking in this sort of ambient light.
I also agree that TAv is Pentax's gift to bird photography (some would say the same about Hyper-program mode), because you often need to adjust both aperture and shutter speed. You can cap the ISO band at 1600 or 3200, where the K-1 should still be generally very good. One thing I love about the KP is the ability to set the ISO with the third wheel - I think you can do this with the K-1 too? So you have all three settings at your fingertips.
You can do a bit in post, especially with low ISO. This one was in similar flat light, with the humble K-S2 and DA L 55-300mm f4-5.8 at 260mm, f8, 1/400th, 100 ISO. RAW file converted with no corrections.
After cropping and processing in DxO PL5 and Nik Color Efex Pro.
Still not great, but OK. The low ISO offered good scope for improving contrast. It's worth trying out the Nik Collection if you haven't already done so (it works as a plugin for LR). The free Google version is still available if you don't want to pay for the DxO version (there's not much difference between them). I find that some of the filters in Color Efex do things that are hard to replicate in PL, particularly Detail Extractor, the contrast filters (e.g. Tonal Contrast, Pro Contrast), Brilliance/Warmth and Darken/Lighten Center.